The mean length of an object is 5 cm. Which of the following measurements is most accurate?

The correct option is 4.9 cm.

To understand why this is the most accurate measurement, let us look at the concept of accuracy in physics and measurement.

1. What is Accuracy?
Accuracy refers to how close a measured value is to the true or accepted value (which is the mean length in this case). The closer a measurement is to the true value, the more accurate it is. Therefore, we need to find which of the given options has the smallest absolute difference (or error) from the mean value of 5 cm.

2. Calculating the Absolute Error for Each Option:
Let the true mean value be $\mu =5\text{cm}$.
We calculate the absolute difference $|\text{Measured Value}-\mu |$ for each option:

• For 4.9 cm:
$|4.9-5|=0.1\text{cm}$

• For 4.805 cm:
$|4.805-5|=0.195\text{cm}$

• For 5.25 cm:
$|5.25-5|=0.25\text{cm}$

• For 5.4 cm:
$|5.4-5|=0.4\text{cm}$

3. Conclusion:
Comparing the absolute errors:
0.1 cm (for 4.9 cm) < 0.195 cm < 0.25 cm < 0.4 cm.
Since 4.9 cm has the smallest deviation (0.1 cm) from the true mean length of 5 cm, it is the most accurate measurement.